A fragmented Supreme Court yesterday appeared to give qualified approval to the widespread police practice in airports of stopping travelers who fit a "drug courier profile."

But the justices imposed stringent limitations on the questioning that can follow such a stop and threw out the conviction of a man caught at Miami International Airport carrying two suitcases full of marijuana.

The usefulness of the decision, which was expected to resolve a major debate about the law enforcement technique, was limited by the absence of a majority for any single point of view. Five justices wrote separately in yesterday's case, prompting one member of the court to refer to it as being about as clear as an "impressionist painting."

A "drug courier profile," pioneered by the U.S. Drug Enforcement Administration, is a list of behavior characteristics authorities say are commonly exhibited by people trafficking in drugs. While each characteristic may mean nothing independently, a person displaying a number of them becomes suspect.

Mark Royer, the defendant in yesterday's case, displayed five of the characteristics when he was stopped in 1978 in the Miami airport: he was carrying heavy American Tourister lugggage; he was between 25 and 35 years old; he appeared pale and nervous--"looking around at other people"; he paid for his ticket in cash with a large number of bills, and he gave only a name--no address--on his luggage identification tag.

Dade County (Fla.) detectives asked Royer for his driver's license and airline ticket. When the names on each turned out to be different (another "characteristic" in the profile) they informed him that he was a narcotics suspect. He agreed to accompany them to a room near the airport concourse.

He then agreed to the opening of his luggage, which revealed 50 pounds of marijuana. The Florida District Court of Appeal threw out his conviction for possession of the drugs on the grounds that the episode in the room constituted an illegal arrest--an arrest made without "probable cause" to believe the suspect guilty of the crime.

At least eight members of the court appeared in agreement that the stop, based on the "drug courier profile," was permissible. Law enforcement officers do not violate the Fourth Amendment's restraint on unreasonable stops "by merely approaching an individual on the street or in another public place, by asking him if he is willing to answer some questions, by putting questions to him if the person is willing to listen. . . , " Justice Byron R. White, joined by three other justices, wrote in the controlling plurality opinion.

Police had "adequate grounds for suspecting Royer of carrying drugs and for temporarily detaining him and his luggage while they attempted to verify or dispel their suspicions," he said.

Those words were taken yesterday by Florida officials as an endorsement of stops based on the courier profile, though federal government lawyers disputed that interpretation. There was less agreement among the justices on the reasons why White then chose to rule in Florida vs. Royer that the suitcases were inadmissible in court as the product of an illegal arrest.

White said "the investigative methods employed should be the least intrusive means reasonably available to verify or dispel the officer's suspicion in a short period of time." In Royer's case, he said, police crossed the line when they informed him he was a suspect, checked his ticket and driver's license and brought him to the room for questioning. The detention then became an arrest, White said, illegal because the suspicions--based only on the profile characteristics--were inadequate to justify an arrest.